On the Nonlinear Stability and Instability of the Boussinesq System for Magnetohydrodynamics Convection

Autor: Dongfen Bian
Jazyk: angličtina
Rok vydání: 2020
Předmět:
Zdroj: Mathematics, Vol 8, Iss 7, p 1049 (2020)
Druh dokumentu: article
ISSN: 2227-7390
DOI: 10.3390/math8071049
Popis: This paper is concerned with the nonlinear stability and instability of the two-dimensional (2D) Boussinesq-MHD equations around the equilibrium state ( u ¯ = 0 , B ¯ = 0 , θ ¯ = θ 0 ( y ) ) with the temperature-dependent fluid viscosity, thermal diffusivity and electrical conductivity in a channel. We prove that if a + ≥ a − , and d 2 d y 2 κ ( θ 0 ( y ) ) ≤ 0 or 0 < d 2 d y 2 κ ( θ 0 ( y ) ) ≤ β 0 , with β 0 > 0 small enough constant, and then this equilibrium state is nonlinearly asymptotically stable, and if a + < a − , this equilibrium state is nonlinearly unstable. Here, a + and a − are the values of the equilibrium temperature θ 0 ( y ) on the upper and lower boundary.
Databáze: Directory of Open Access Journals
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